Prior to June 11, 1945, Florida used a system of highways with designations assigned by the Florida legislature. The earliest evidence . . . of the numbering system is from a 1917 State Road map, listing old FL 1 though old FL 12. It is possible that the route numbers were not actually posted until 1923. The actual practice of assigning routes by legislation started in 1923. The lower numbers were the primary routes of the early 1920's. Other numbers were added later, up to FL 601. The old Florida state highway sign was a blue diamond. This type of sign was also retired in 1945 in favor of a square sign with a state outline, similar to the style in use today.

According to this source, even after at least 60 years there are still several blue diamond signs alongside Florida roadways.

UPDATE: Robert V. Droz, whose website is quoted above, emails with a correction, "There are no blue diamond signs left, those old numbers live on in the street signs along the routes."

Check out Mr. Droz's Florida Auto Trails website.